Disproving the conjecture on structural physical approximation to optimal decomposable entanglement witnesses

TL;DR

This paper disproves a conjecture that structural physical approximations to optimal entanglement witnesses are always separable, showing the conjecture only holds for extremal decomposable witnesses.

Contribution

It provides a counterexample to the conjecture and clarifies the conditions under which the conjecture is valid.

Findings

Disproves the general conjecture for optimal entanglement witnesses.

Shows the conjecture holds only for extremal decomposable witnesses.

Advances understanding of the structure of entanglement witnesses.

Abstract

We disprove the conjecture that structural physical approximations to optimal entanglement witnesses are separable states. The conjecture holds true for extremal decomposable entanglement witnesses.